(Solved): UNIVERSITY OF NAIROBI DMS 501: BUSINESS QUANTITATIVE ANALYSIS SEPT DEC, 2023 SEMESTER ASSIGNMEN ...

UNIVERSITY OF NAIROBI DMS 501: BUSINESS QUANTITATIVE ANALYSIS SEPT DEC, 2023 SEMESTER ASSIGNMENT 1 - DESCRIPTIVE STATISTICS DUE DATE: $8^{\mathrm{TH}}$ NOVEMBER, 2023 Question 1 In a study to analyse performance in a 2022 examination series the following scores in a percentage were compiled for a sample of 100 candidates. $42,51,52,53,61,62,63,64,71,72,81,46,53,54,55,63,64,65,66,73,74,82,48,57,58,59,67,68,69,77,78,87,43,5$ $4,56,64,65,66,67,74,75,84,47,52,53,54,62,63,64,65,72,73,82,45,56,57,58,66,67,68,69,76,77,86,44,55,56$, $57,65,66,67,75,76,85,49,50,51,52,60,61,62,70,71,51,52,53,61,62,63,71,72,58,59,57,68,69,67,78,79,80$ a) Arrange the data in equal classes of size 10 starting from 40 percent. b) Using an ogive for the data, find i) The approximate percentage of the candidates who passed the examination if the pass mark was 62.5 percent. ii) The pass marks if 90 percent of the candidate passed examination. c) Verify whether it would be appropriate to use the properties of normal probability distribution in analyzing the data (perform acid test of normality i.e skewness and kurtosis). Question 2 Two brands of tyres were tested for their life and the following results were obtained: Required: i. Compute the means of the two brands of tyres ii. Compute the standard deviations of the two brands of tyres iii. If consistency is the criterion, which brand is preferable?